The Delphi Method: Techniques and Applications

Cross-impact analysis is a method for revising estimated probabilities of future events in terms of estimated interactions among those events. This Report presents anelementary cross-impact model where the cross-impacts are formulated as relativeprobabilities. Conditions are derived for the consistency of the matrix of relative probabilities of n events. An extension also provides a necessary condition for thevector of absolute probabilities to be consistent with the relative probability matrix. Anaveraging technique is formulated for resolving inconsistencies in the matrix, and a nearest-point computation derived for resolving inconsistencies between the set ofabsolute probabilities and the matrix.Although elementary, the present model clarifies some of the conceptual problems associated with cross-impact analysis, and supplies a relatively sound basisfor revising probability estimates in the limited case where interactions can beapproximated by relative probabilities.